Number 6 on Exam 2

asmith14 — Mon, 28 Jul 2014 14:47:43 -0500

I have a question on number six from the last test because I am unable to figure out what I did wrong. The question was to use Lagrange multipliers to find the extremes of $f(x,y)=x+y^2$ subject to the constraint $x^2+y^2=1$. Can someone please offer any help as to where I went wrong or any tips that might help for the final. I do not know how to draw the graph on here but this is my work for part C. $$\nabla f=<1,2y>$$ $$\nabla g=<2x,2y>$$ then from those I got $$1=2\lambda x$$ $$2y=2\lambda y$$ $$x^2+y^2=1$$ and solved and found $$x=1/2\lambda$$ $$y=\pm \sqrt {3/4}$$ $$\lambda =1$$ then I put those together to find my critical points to be $$(1/2,\sqrt {3/4)}:{max}$$ $$(1/2,-\sqrt {3/4)}:{min}$$. Please let me know if you have any ideas I to what I should of done and how to fix it.

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Number 6 on Exam 2